Many rotationally symmetric lenses have been described over the years, and most of them are capable of imaging an azimuthal field of 360° about the axis of rotation, also called the optical axis. What distinguishes panoramic lenses is that their field of view is not measured from 0° at the optical axis to their maximum field, rather their field of view is measured with respect to a plane perpendicular to the optical axis. This plane is often referred to as the horizontal plane. For example, for a panoramic lens, the field of view may be referred to as +5°/−20°, which means that the picture includes up to five degrees above the horizontal and twenty degrees below.
Means of obtaining panoramic views such as use of multiple cameras or scanning a single camera have been proposed. However, a major problem with multiple cameras is stitching the images together to form a panorama. Carefully scanning a single camera can alleviate this difficulty, but accurately moving a camera introduces an additional set of difficulties.
Optical systems may be divided into three categories: dioptric, catoptric and catadioptric. The first of these categories, dioptric, contains all optical systems that have only transmissive elements. Similarly, catoptric optical systems have only reflective elements. Catadioptric optical systems have both transmissive and reflective elements, and may be divided into two subcategories. One of these subcategories includes all optical systems that have within them a single element that both reflects and transmits light, while the other is restricted to elements that either reflect or transmit, but not both. The latter subcategory includes optical systems that have mirrors that transmit light either around their periphery or through a hole, as long as that light is not refracted by the mirror substrate.
Dioptric wide angle lenses, such as fisheye lenses, have been known to achieve larger than hemispherical fields of view, with half field angles up to 140°, measured from the optical axis. Such lenses are frequently described by their full field angle, so a lens with the half field angle of 140° would be called a 280° fisheye. As a panoramic lens, it would be described as a +90°/−50° lens. However, fisheye lenses often have significant image compression (distortion) at the edge of the field of view, resulting in decreased resolution in the portion of the field near the horizontal plane. U.S. Pat. No. 5,185,667 to Zimmerman describes the use of a fisheye lens as a panoramic lens.
Catoptric optical systems have also been proposed as panoramic lenses. For example, U.S. Pat. No. 5,920,376 to Bruckstein et al. describes cameras that are purely catoptric, consisting only of one or more mirrors and a pinhole camera arrangement. A significant problem with this type of system is that a pinhole does not allow much light to get to the image. The pinhole is generally required to reduce aberrations to an acceptable level. Another way to express this problem is that catoptric panoramic lenses are generally restricted to large F-numbers or small numerical apertures by their aberrations.
U.S. Pat. No. 1,616,279 to Parodi and U.S. Pat. No. 2,638,033 to Buchele describe catadioptric panoramic optical systems. Although there are certain advantages to such designs, an overriding difficulty is the difficulty and complexity of fabricating the elements.
Catadioptric panoramic optical systems with only reflecting or transmitting elements are known. Multiple-catadioptric systems may be capable of high performance, but suffer the difficulty of aligning the mirrors and keeping them in alignment. One example of a complex mirror alignment is disclosed in U.S. Pat. No. 5,627,675 to Davis et al. Although blur sizes of less than 10 microns at F/1.5 are shown, the optical arrangement is extremely complex.
Single mirror catadioptric panoramic optical systems have been described in various patents. U.S. Pat. No. 2,244,235 to Ayres proposes a spherical mirror, with the possibility of corrected for aberrations. U.S. Pat. No. 2,299,682 to Conant discloses parabolic mirrors and others of modified conical curvature, e.g., conical and spherical forms. U.S. Pat. No. 2,371,495 to Benford deviates from simple quadric forms and prescribes a mirror that is shaped to create uniform illumination versus angle.
Aberrations, as mentioned in the Ayres U.S. Pat. No. 2,244,235 patent cited above or U.S. Pat. No. 2,430,595 to Young, are important factors in designing a panoramic optical system. They may be categorized as chromatic or monochromatic aberrations. Chromatic aberrations cause images of points to be spread out according to the wavelength of light. Such aberrations can be eliminated by using only mirrors or may be reduced by using achromatic lenses.
Monochromatic aberrations are typically divided into primary and higher order aberrations. Primary aberrations include spherical aberration, which introduces a blur to the image that is constant across the field of view. Coma and astigmatism blur the image with a magnitude that varies linearly and quadratically with field angle, respectively. Field curvature causes the best image not to lie on a plane, so that an image formed on a flat piece of film or a flat array detector is blurred. Distortion does not blur the image, but causes a magnification that varies as the cube of the field angle, so that the image of a square has curved sides.
Such aberrations adversely affect the quality of the images. The aberrations that are most significant in panoramic lenses are astigmatism and distortion because the field angle is so large. Because it does not blur the image, distortion of up to roughly ten or twenty percent is often tolerable. This leaves astigmatism as the most important aberration in panoramic lenses.
Several ways to reduce astigmatism to an acceptable level have been proposed. One way is to use an optical system with several mirrors, such as described in the Davis et al. U.S. Pat. No. 5,627,675 patent. Another way is to use a very slow (high F/number) optical system, such as the pinhole camera mentioned in the Bruckstein et al. U.S. Pat. No. 5,920,376 patent. The former method is impractical to manufacture for commercial purposes due to its complexity, and the latter can be impractical for photography because it requires the scene to be brightly illuminated. Another approach is described in U.S. Pat. No. 7,242,425 to Driscoll, Jr. et al., which is incorporated herein by reference. Driscoll, Jr. et al. U.S. Pat. No. 7,242,425 proposes the use of a parabolic mirror with an astigmatism correction lens.
Specially shaped mirrors for catadioptric panoramic lenses have been proposed with a variety of design rationales. U.S. Pat. No 2,371,495 to Benford proposed a shape that corrects for cosine falloff of illumination. U.S. Pat. No. 6,304,285 to Geng proposes a hyperbolic mirror for single virtual viewpoint. U.S. Pat. No. 6,412,961 to Hicks suggests a mirror form that maps a distance in object space to a distance on the image. U.S. Pat. No. 6,856,472 to Herman discloses another type of mirror design. Such designs deal primarily with distortion, which may be described generally as the mapping of angles or distances in object space to angles or distances in image space. U.S. Pat. No. 2,244,235 to Ayres mentions that the shape of the surfaces and shells of spherical reflectors may be corrected for aberration, but provides no description of the particular type of aberration, or how to correct it.